Magnetic fields of precise geometry are needed in medical magnetic imaging applications, like magnetic resonance imaging (MRI) and magnetoencephalography (MEG). Recently, also combination of the two imaging techniques has been proposed (“Microtesla MRI on the human brain combined with MEG”, Vadim S. Zotev et al, Journ. Mag. Res. 194, pp 115-120, 2008).
In the MRI method the part of the human body that is studied is exposed to a uniform magnetic field, and to gradients of the field for decoding of the spatial information contained in the MRI signal. The geometry of the measuring field essentially contributes to the signal quality and geometric precision of the resulting MRI image. An ideal measuring field is free of field derivatives higher than first.
In the MEG method the very weak magnetic signals resulting from the functioning of the human brain are recorded by sensors located around the head. One of the main problems in this technique is the protection of the measuring device against the environmental magnetic interference the strength of which may exceed the signals of interest by seven to eight orders of magnitude. This magnetic shielding problem can be solved by active compensation methods that counteract the interference using coil systems tailored to produce counter fields that very precisely match the geometry of the interference fields (see patent application PCT/FI2005/000090).
The interference fields in a typical MEG recording environment are relatively uniform and smooth. “Smooth” means here that the fields comprise of spatially uniform field components and only low order spatial derivatives of these components. Spatial derivatives higher than first order, say, are of very small amplitude in the interference. This is so because these fields arise from sources tens of meters away from the recording device, and are additionally smoothed by the magnetically shielding room (MSR) housing the MEG device. Therefore, the fields used to counteract these interference fields in an active compensation arrangement must also be smooth and tailored to optimally match the interference field geometry. This enables maximal compensation of the interference over relatively large volume of the size of the human head.
In both MRI and MEG methods the coil systems must be located relatively close to the measuring device. This way the currents needed to create the measuring and counteracting fields stay reasonably small. Furthermore, if a feedback principle is used for the active compensation the compensation coils must necessarily be inside the MSR (PCT/FI2005/000090). Placing the coils outside of the MSR would cause extra delay and lead to unstable feedback loop.
The requirements that the fields must be uniform or smooth over a large measuring volume, and must be generated by coils located near this volume, at a distance of one to two meters only, are contradictory. Field profiles generated by close-by coils necessarily contain second and higher derivatives, and the coils must be carefully designed to produce smooth fields and gradients over a volume as large as the size of human head, for example.
A well-known, elementary example toward the solution of this kind of coil design problem are the so called Helmholz and Maxwell pairs: By properly choosing the distance between two circular, coaxial coils of same size one can create, mid between the two coils, an axial field Bx uniform up to the fourth derivative dBx/dx is d4Bx/dx4. The coil assembly optimized this way is called a Helmholz-pair. The first non-zero derivative of its field is d4Bx/dx4. A spatially constant axial derivative dBx/dx smooth up to fifth derivative is created by a coil set called a Maxwell-pair where the first non-zero odd derivative beyond dBx/dx is d5Bx/dx5. But, to generate uniform magnetic fields in all three spatial directions (Bx, By, Bz), and their derivatives—constant over a macroscopic volume—one must design a coil assembly that simultaneously controls the magnetic fields in the three orthogonal directions, the five independent first derivatives of these components, and the seven independent second derivatives etc. This requirement formulates a kind of “generalized Helmholz/Maxwell coil design problem”. Obviously, to solve this problem, a larger number of independent coils is needed than the two coils in the Helmholz and Maxwell cases.
For practical applications this coil design problem is further complicated by the presence of magnetic materials in the vicinity of the coils, and specifically in MEG, by the presence of the MSR. Its walls contain material of high magnetic susceptibility which gets magnetized in the field produced by the current in the coils. This results in a considerable scattered field that is added to the direct field of the coils. The susceptibility values of the MSR wall elements and the characteristics of the joints between the elements vary from one MSR to another and may even change with time. Therefore designing the coil assembly by a mere calculation would require measurement and characterization of the room structure and magnetic properties of the wall elements in such a detailed manner that it is practically impossible.